Universality in an integer quantum Hall transition

Abstract

An integer quantum Hall effect transition is studied in a modulation-doped $p$-SiGe sample. In contrast to most examples of such transitions the longitudinal and Hall conductivities at the critical point are close to 0.5 and 1.5 ${(e}^{2}/h),$ the theoretically expected values. This allows the extraction of a scattering parameter, describing both conductivity components, which depends exponentially on filling factor. The strong similarity of this functional form to those observed for transitions into the Hall insulating state and for the $B=0$ metal-insulator transition implies a universal quantum-critical behavior for the transitions. The observation of this behavior in the integer quantum Hall effect, for this particular sample, is attributed to the short-ranged character of the potential associated with the dominant scatterers.